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6000 matmuls CG unprec 2000 matmuls CG prec (4000 eo muls) 1050 matmuls PGCR on 16^3 x 32 x 8 m=.01 Substantial effort on timing and logging infrastructure
176 lines
4.7 KiB
C++
176 lines
4.7 KiB
C++
#ifndef GRID_PREC_GCR_H
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#define GRID_PREC_GCR_H
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///////////////////////////////////////////////////////////////////////////////////////////////////////
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//VPGCR Abe and Zhang, 2005.
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//INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
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//Computing and Information Volume 2, Number 2, Pages 147-161
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//NB. Likely not original reference since they are focussing on a preconditioner variant.
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// but VPGCR was nicely written up in their paper
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///////////////////////////////////////////////////////////////////////////////////////////////////////
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namespace Grid {
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template<class Field>
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class PrecGeneralisedConjugateResidual : public OperatorFunction<Field> {
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public:
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RealD Tolerance;
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Integer MaxIterations;
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int verbose;
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int mmax;
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int nstep;
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int steps;
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LinearFunction<Field> &Preconditioner;
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PrecGeneralisedConjugateResidual(RealD tol,Integer maxit,LinearFunction<Field> &Prec,int _mmax,int _nstep) :
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Tolerance(tol),
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MaxIterations(maxit),
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Preconditioner(Prec),
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mmax(_mmax),
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nstep(_nstep)
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{
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verbose=1;
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};
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void operator() (LinearOperatorBase<Field> &Linop,const Field &src, Field &psi){
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psi=zero;
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RealD cp, ssq,rsq;
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ssq=norm2(src);
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rsq=Tolerance*Tolerance*ssq;
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Field r(src._grid);
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steps=0;
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for(int k=0;k<MaxIterations;k++){
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cp=GCRnStep(Linop,src,psi,rsq);
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if ( verbose ) std::cout<<GridLogMessage<<"VPGCR("<<mmax<<","<<nstep<<") "<< steps <<" steps cp = "<<cp<<std::endl;
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if(cp<rsq) {
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Linop.HermOp(psi,r);
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axpy(r,-1.0,src,r);
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RealD tr = norm2(r);
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std::cout<<GridLogMessage<<"PrecGeneralisedConjugateResidual: Converged on iteration " <<steps
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<< " computed residual "<<sqrt(cp/ssq)
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<< " true residual " <<sqrt(tr/ssq)
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<< " target " <<Tolerance <<std::endl;
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return;
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}
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}
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std::cout<<GridLogMessage<<"Variable Preconditioned GCR did not converge"<<std::endl;
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assert(0);
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}
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RealD GCRnStep(LinearOperatorBase<Field> &Linop,const Field &src, Field &psi,RealD rsq){
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RealD cp;
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RealD a, b, c, d;
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RealD zAz, zAAz;
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RealD rAq, rq;
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GridBase *grid = src._grid;
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Field r(grid);
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Field z(grid);
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Field tmp(grid);
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Field ttmp(grid);
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Field Az(grid);
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////////////////////////////////
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// history for flexible orthog
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////////////////////////////////
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std::vector<Field> q(mmax,grid);
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std::vector<Field> p(mmax,grid);
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std::vector<RealD> qq(mmax);
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//////////////////////////////////
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// initial guess x0 is taken as nonzero.
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// r0=src-A x0 = src
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//////////////////////////////////
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Linop.HermOpAndNorm(psi,Az,zAz,zAAz);
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r=src-Az;
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/////////////////////
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// p = Prec(r)
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/////////////////////
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Preconditioner(r,z);
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std::cout<<GridLogMessage<< " Preconditioner in " << norm2(r)<<std::endl;
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std::cout<<GridLogMessage<< " Preconditioner out " << norm2(z)<<std::endl;
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Linop.HermOp(z,tmp);
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std::cout<<GridLogMessage<< " Preconditioner Aout " << norm2(tmp)<<std::endl;
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ttmp=tmp;
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tmp=tmp-r;
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std::cout<<GridLogMessage<< " Preconditioner resid " << std::sqrt(norm2(tmp)/norm2(r))<<std::endl;
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/*
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std::cout<<GridLogMessage<<r<<std::endl;
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std::cout<<GridLogMessage<<z<<std::endl;
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std::cout<<GridLogMessage<<ttmp<<std::endl;
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std::cout<<GridLogMessage<<tmp<<std::endl;
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*/
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Linop.HermOpAndNorm(z,Az,zAz,zAAz);
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//p[0],q[0],qq[0]
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p[0]= z;
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q[0]= Az;
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qq[0]= zAAz;
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cp =norm2(r);
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for(int k=0;k<nstep;k++){
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steps++;
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int kp = k+1;
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int peri_k = k %mmax;
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int peri_kp= kp%mmax;
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rq= real(innerProduct(r,q[peri_k])); // what if rAr not real?
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a = rq/qq[peri_k];
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axpy(psi,a,p[peri_k],psi);
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cp = axpy_norm(r,-a,q[peri_k],r);
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std::cout<<GridLogMessage<< " VPGCR_step resid" <<sqrt(cp/rsq)<<std::endl;
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if((k==nstep-1)||(cp<rsq)){
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return cp;
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}
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Preconditioner(r,z);// solve Az = r
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Linop.HermOpAndNorm(z,Az,zAz,zAAz);
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Linop.HermOp(z,tmp);
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tmp=tmp-r;
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std::cout<<GridLogMessage<< " Preconditioner resid" <<sqrt(norm2(tmp)/norm2(r))<<std::endl;
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q[peri_kp]=Az;
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p[peri_kp]=z;
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int northog = ((kp)>(mmax-1))?(mmax-1):(kp); // if more than mmax done, we orthog all mmax history.
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for(int back=0;back<northog;back++){
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int peri_back=(k-back)%mmax; assert((k-back)>=0);
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b=-real(innerProduct(q[peri_back],Az))/qq[peri_back];
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p[peri_kp]=p[peri_kp]+b*p[peri_back];
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q[peri_kp]=q[peri_kp]+b*q[peri_back];
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}
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qq[peri_kp]=norm2(q[peri_kp]); // could use axpy_norm
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}
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assert(0); // never reached
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return cp;
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}
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};
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}
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#endif
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